Fabry-Perot Fourier transform spectrometer

ABSTRACT

A spatial Fourier transform spectrometer is disclosed. The Fourier transform spectrometer includes a Fabry-Perot interferometer with first and second optical surfaces. The gap between the first and second optical surfaces spatially varies in a direction that is orthogonal to the optical axis of the Fourier transform spectrometer. The Fabry-Perot interferometer creates an interference pattern from input light. An image of the interference pattern is captured by a detector, which is communicatively coupled to a processor. The processor is configured to process the interference pattern image to determine information about the spectral content of the input light.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/958,312, filed Dec. 1, 2010, and entitled “FABRY-PEROT FOURIERTRANSFORM SPECTROMETER,” which claims priority to the following UnitedStates provisional patent applications: U.S. Provisional PatentApplication No. 61/283,519, filed Dec. 2, 2009, and entitled “SPATIALLYVARIABLE ETALON FOR SPECTROSCOPY AND SPECTRAL IMAGING”; and U.S.Provisional Patent Application No. 61/345,549, filed May 17, 2010, andentitled “A FABRY-PEROT INTERFEROMETER WITH A SPATIALLY VARIABLERESONANCE GAP EMPLOYED AS A FOURIER TRANSFORM SPECTROMETER.” Each of theforegoing patent applications is hereby incorporated herein by referencein its entirety to be considered part of this specification.

BACKGROUND OF THE INVENTION Field of the Invention

The invention relates to the field of spectroscopy including, forexample, Fourier transform spectroscopy.

Description of the Related Art

Fourier transform spectroscopy is a technique that can be used forobtaining information about the spectral content of light from a source.Many Fourier transform spectrometers (FTS) employ a Michelsoninterferometer and measure the spectrum of light that is encoded in atime-varying signal that results from the interaction of the input lightwith the interferometer. In a Michelson FTS the interference pattern issampled in time. The Michelson FTS uses a moving mirror that causes aninput beam, which is split into two arms and then recombined, toexperience a time varying optical path difference (OPD) between the twoarms. Illuminated by monochromatic light, the detector response to thistime varying OPD is a sinusoidal signal whose period is a function ofthe rate of change of the OPD and the wavelength of the incident light.The wavelength of the incident light is recovered from the sampledsignal by precise knowledge of the rate of change of the OPD, usuallyusing a reference laser signal. Illumination by multiple wavelengthsproduces a resultant pattern that is additive; the intensities of theindividual wavelengths are recovered using the Fourier transform afterappropriate preprocessing. The transformation from sampled interferencepattern (i.e., the interferogram) to spectrum is well-established.

Another type of FTS is the spatial FTS, where the spectrum of the inputlight is encoded in a spatial pattern sampled by a detector array. Aspatial FTS may use optics to produce a gradient in OPD across adetector array, for example, by slight deviations of mirrors orbeamsplitters relative to perfect symmetry. The interaction ofilluminating light with this gradient in OPD produces an interferencepattern that is sampled by the array. The interferogram is calibrated inwavelength (i.e., the slope of the OPD is determined) using a knownmonochromatic source (e.g., light transmitted through an interferencefilter). Once sampled and corrected for non-uniformities in response ofthe detector array elements, data processing can be similar to theMichelson FTS data processing.

SUMMARY OF THE INVENTION

In some embodiments, a Fourier transform spectrometer comprises: aFabry-Perot interferometer to create an interference pattern using inputlight; a detector positioned with respect to the Fabry-Perotinterferometer to capture an image of the interference pattern, thedetector comprising a plurality of detection elements, and defining anoptical axis that is orthogonal to the detector; and a processor that iscommunicatively coupled to the detector, the processor being configuredto process the interference pattern image to determine information aboutthe spectral content of the light, wherein the Fabry-Perotinterferometer comprises first and second optical surfaces that arepartially transmissive and partially reflective to the light, the firstand second optical surfaces defining a resonant cavity therebetween, thedistance between the first and second optical surfaces being spatiallyvariable in a first transverse direction that is orthogonal to theoptical axis.

In some embodiments, a method of determining the spectral content ofinput light comprises: creating an interference pattern from input lightusing a Fabry-Perot interferometer; creating an interference patternimage using a detector that is positioned with respect to theFabry-Perot interferometer to capture an image of the interferencepattern, the detector comprising a plurality of detection elements, anddefining an optical axis that is orthogonal to the detector; andprocessing the interference pattern image using a processor to determineinformation about the spectral content of the light, wherein theFabry-Perot interferometer comprising first and second optical surfacesthat are partially transmissive and partially reflective to the light,the first and second optical surfaces defining a resonant cavitytherebetween, the distance between the first and second optical surfacesbeing spatially variable in a first transverse direction that isorthogonal to the optical axis, and wherein the interference patternimage is captured during a period of time in which characteristics ofthe Fabry-Perot interferometer are not intentionally varied.

BRIEF DESCRIPTION OF THE DRAWINGS

Certain aspects, advantages, and features of the invention are describedherein. It is to be understood, however, that not necessarily all suchaspects, advantages, and features are necessarily included or achievedin every embodiment of the invention. Thus, the invention may beembodied or carried out in a manner that includes or achieves oneaspect, advantage, or feature, or group thereof, without necessarilyincluding or achieving other aspects, advantages, or features as may betaught or suggested herein. Certain embodiments are illustrated in theaccompanying drawings, which are for illustrative purposes only.

FIG. 1 is a schematic diagram of the operation of a Fabry-Perotinterferometer that has a spatially invariant gap between the twooptical surfaces of the interferometer.

FIG. 2 illustrates the output, in response to a collimated input beam,of a Fabry-Perot interferometer that has a spatially invariant gapbetween the two optical surfaces of the interferometer (top), as well asthat of a Fabry-Perot interferometer that has a spatially varying gapbetween its two optical surfaces (bottom).

FIG. 3 is a block diagram of an embodiment of a Fourier transformspectrometer that uses a Fabry-Perot interferometer with a spatiallyvarying gap between two optical surfaces to create an interferencepattern.

FIG. 4 illustrates an embodiment of a Fabry-Perot interferometer thatcan be used in the Fourier transform spectrometer of FIG. 3.

FIG. 5 illustrates another embodiment of a Fabry-Perot interferometerthat can be used in the Fourier transform spectrometer of FIG. 3.

FIG. 6 is a schematic diagram of a Fourier transform spectrometer thatuses a Fabry-Perot interferometer with a spatially varying gap, and thatincludes a light collection optical system, and an interference patternrelay optical system.

FIG. 7 is an example plot that illustrates the transmission ofmonochromatic light through a Fabry-Perot interferometer with aspatially varying gap between two optical surfaces, the transmissionbeing shown for a range of reflectance values of the optical surfaces.

FIG. 8 is an example plot that illustrates the Fourier transform of thecurve from FIG. 7 that corresponds to a Fabry-Perot interferometerhaving 18% reflecting optical surfaces.

FIG. 9 is an example plot that illustrates the peak Fourier magnitude ofa monochromatic source as a function of surface reflectance for aFabry-Perot interferometer that has a spatially varying gap.

FIG. 10 is an example plot that shows an estimate of absolute efficiencyfor a Fourier transform spectrometer that uses a Fabry-Perotinterferometer with a spatially varying gap.

FIG. 11 is an example interference pattern image from a Fabry-Perotinterferometer with a spatially varying gap that illustrates the effectof incidence angle on the fringe period for a monochromatic input beam.

FIG. 12 is an example interference pattern image that shows the signalat each incidence angle integrated over the range from 0° to the givenincidence angle.

FIG. 13 is an example plot that shows the resolving power, as a functionof f-number of the input light, for a Fabry-Perot interferometer with aspatially varying gap filled with air.

FIG. 14 is an example plot that shows the resolving power, as a functionof the effective f-number of the input light, for a germaniumFabry-Perot etalon with a spatially varying gap.

FIG. 15 is an example plot that shows the measured spectrum offluorescent light using a Fourier transform spectrometer with aFabry-Perot interferometer that has a spatially varying gap.

FIG. 16 is a photograph of an embodiment of a Fourier transformspectrometer that uses a Fabry-Perot interferometer with a spatiallyvarying gap.

FIG. 17 is an example interference pattern image obtained using theFourier transform spectrometer of FIG. 16.

FIG. 18 is an example plot of the measured spectrum of a blackbodysource with diethyl ether sprayed into the beam, which was obtainedusing the Fourier transform spectrometer of FIG. 16.

FIG. 19 is an example plot that shows the time variation of the measuredspectrum from FIG. 18.

FIG. 20 is an example interference pattern image produced by a Fouriertransform spectrometer with a Fabry-Perot interferometer that has alinearly spatially varying gap.

FIG. 21 is an example plot of the measured spectrum of a blackbodysource with diethyl ether sprayed into the beam, which was obtainedusing a Fourier transform spectrometer with a Fabry-Perot interferometerthat has a linearly spatially varying gap.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The following disclosure describes embodiments of a type of spatial FTSthat uses a Fabry-Perot interferometer with a spatially varying gapbetween its reflective layers to produce interference, or fringe,patterns that can be processed to obtain information regarding thespectral content of light. In some embodiments, the gap varies in adirection that is orthogonal to the optical axis of the FTS. Thisspatially varying gap can produce a gradient in optical path length at adetector. This gradient in optical path length produces an interferencepattern that, in some embodiments, can be analyzed with conventional FTSdata processing techniques. The disclosure also describes the impact ofthe non-sinusoidal periodic spatial interference pattern that isproduced by some embodiments of the FTS, as well as a choice of layerreflectances to increase or maximize sensitivity, and the effect ofusing the FTS with input light that has a range of incidence angles uponthe interferometer.

FIG. 1 is a schematic diagram of the operation of a Fabry-Perotinterferometer 100 that has a spatially invariant gap between the twooptical surfaces 102, 104 of the interferometer. The Fabry-Perotinterferometer 100 includes a first planar optical surface 102 that ispartially transmissive and partially reflective to the incident ray oflight 106. The Fabry-Perot interferometer 100 also includes a secondplanar optical surface 104 that is likewise partially transmissive andpartially reflective to the light.

The Fabry-Perot interferometer 100 exploits a phenomenon widely observedin nature: modulation of light by wavelength dependent interferencecaused by multiple reflections among optical surfaces. Robert Hookereported this phenomenon with respect to lenses in physical contact withplates. The resultant interference rings are known as Newton's rings,owing to Newton's detailed analysis of the phenomenon. The Fabry-Perotinterferometer 100 exploits this phenomenon by placing two partiallyreflecting surfaces in close proximity, forming a resonant cavity 101. Aray of light 106 that is incident on the pair of surfaces 102, 104 willmultiply reflect within the cavity 101, with interference occurringamong light rays T₁, T₂ (or R₁, R₂) that exit the Fabry-Perotinterferometer 100 after having traversed the cavity 101 a differentnumber of times.

The details of how light is altered as it passes through the cavity 101depend, to first order, upon the length (l) of the space between thereflecting surfaces, their reflectance, the angle of incidence (θ) withrespect to a normal 108, and the refractive index (n) of the medium inthe gap between reflectors 102, 104.

The transmission of the Fabry-Perot interferometer 100 is given by thefollowing equation (written in a form so as to emphasize the role of thephase difference δ in the face of a variable gap):

$\begin{matrix}{T = \frac{R^{2} - {2\; R} + 1}{R^{2} - {2\; R\;\cos\;\delta} + 1}} & (1)\end{matrix}$In this expression, R is the reflectance of the layers and δ is thephase difference between reflections. The variable δ is given by thefollowing expression:

$\begin{matrix}{\delta = {\frac{4\;\pi\; n\;\cos\;\theta}{\lambda}{l(x)}}} & (2)\end{matrix}$where n is the refractive index of the medium in the gap, θ is the angleat which the ray traverses the gap relative to the normal 108, l is thegap thickness (expressed here as an arbitrary function of position inthe x-direction orthogonal to the optical axis, which in this case isparallel with the normal 108), and λ is the wavelength. The wavelengthand gap thickness are in the same units.

In conventional Fabry-Perot interferometers (e.g., 100) the gap is aconstant in the x-direction such that the function l(x) is equal to aconstant. While scanning Fabry-Perot interferometers do vary the gapthickness in time in the longitudinal direction along the optical axis,the gap thickness still remains spatially constant (e.g., in thetransverse directions orthogonal to the optical axis) at each point intime.

Historically, an air or vacuum gap Fabry-Perot device is sometimescalled an interferometer, while a solid-filled gap is sometimes calledan etalon, but the principles of operation are the same, and both willbe referred to interchangeably in this disclosure unless specificallynoted to the contrary.

FIG. 2 illustrates the output, in response to a collimated input beam,of a Fabry-Perot interferometer 200 that has a spatially invariant gapbetween the two optical surfaces of the interferometer (top), as well asthat of a Fabry-Perot interferometer 220 that has a spatially varyinggap between its two optical surfaces (bottom). The bottom portion ofFIG. 2 conceptually illustrates the usage of a Fabry-Perotinterferometer to construct an interference pattern with spatialfringes.

The top portion of FIG. 2 includes a monochromatic point source 210.Light from the monochromatic point source 210 is collimated by a lens211 to create a collimated input beam 212. This collimated beam isincident upon a Fabry-Perot interferometer 200, which has a spatiallyinvariant gap between two optical surfaces, as described above withrespect to FIG. 1. With parallel optical surfaces in the interferometer200, the interference pattern in the output beam 214 is uniform across adetecting screen (in the case of the collimated input beam 212). This isshown in the plot 216 where intensity 218 at the detector is graphed asa function of position on the detector in the x-direction. As is evidentfrom the line 218, since the function l(x) is equal to a constant forthe Fabry-Perot interferometer 200, and since the angle θ is constantfor the collimated input beam 212, the intensity at the detector is alsoconstant in the x-direction per Equations (1) and (2).

In contrast, the bottom portion of FIG. 2 illustrates the output of aFabry-Perot interferometer 220 that has a spatially varying gap betweenits two optical surfaces (illustrated in FIG. 2 as non-parallel lines).In this case, a monochromatic point source 230 emits light that iscollimated by a lens 231 into a collimated input beam 232 that isincident upon the Fabry-Perot interferometer 220. The Fabry-Perotinterferometer 220 creates an interference pattern 238 in the outputbeam 234. The interference pattern 238 is shown in the plot 236 whereintensity at the detector is plotted as a function of position on thedetector in the x-direction. Since the plates of the Fabry-Perotinterferometer 220 are not parallel, but are instead tilted with respectto one another, the gap thickness l in Equation 2 varies linearly withposition in the x-direction. Accordingly, per Equations (1) and (2), thetransmitted interference pattern is a periodic function, which producesa periodic signal 238 on the detector.

One characteristic of a spatial FTS is that it creates awavelength-dependent spatial fringe pattern (e.g., a periodic fringepattern), which is spatially sampled by a detector array and isprocessed using, for example, a Fourier transform to determine thespectrum. Some conventional FTS instruments use eitherbeamsplitter-based interferometers, or birefringent crystals withappropriate polarizers to produce the fringe pattern. However, asillustrated in the bottom portion of FIG. 2, the spatial FTS describedherein uses a Fabry-Perot interferometer with a spatially varying gap toproduce the fringe pattern.

FIG. 3 is a block diagram of an embodiment of a Fourier transformspectrometer 350 that uses a Fabry-Perot interferometer 320 with aspatially varying gap between two optical surfaces to create aninterference pattern 334. The Fourier transform spectrometer 350 canreceive input light 332 from any source whose spectral content isdesired to be measured. Embodiments of the FTS described herein canoperate in, for example the visible and infrared regions of theelectromagnetic spectrum. The input light 332 is directed to theFabry-Perot interferometer 320 with a spatially varying gap.

The Fabry-Perot interferometer 320 creates an interference pattern 334,which is directed to a detector 340. The detector 340 may include aplurality of detecting elements arranged in a one-dimensional lineararray in order to simultaneously spatially sample the interferencepattern 334 at different locations. The detecting elements can also bearranged in a two-dimensional array, for example, in the case of theFourier transform spectrometer 350 being an imaging spectrometer. Inthis way, the detector 340 creates an interference pattern image 338.The detector 340 can include a number of detecting elements arranged ina plane that is, for example, orthogonal to the optical axis of theinstrument. The detector 340 can also have a higher-dimensionality(e.g., the detecting elements could be arranged on the surface of acylinder or other non-planar surface).

In some embodiments, the Fabry-Perot interferometer 320 is designed soas to produce symmetric interferograms, where the OPD function acrossthe detector array is linear and is equal to zero at the center of thefringe pattern. The geometry shown in the bottom portion of FIG. 2 doesnot reach zero OPD. To achieve zero OPD, the two surfaces meet inoptical contact. This can be achieved in many different ways, two ofwhich are shown in FIGS. 4 and 5.

The detector is communicatively coupled to an image processor 342. Theimage processor 342 receives the interference pattern image from thedetector and executes image processing algorithms to convert theinterference pattern image 338 from the spatial domain to the frequencydomain. The image processor 342 can perform this conversion using manydifferent techniques, including, for example, a Fourier transform. Insome embodiments, the discrete Fourier Transform can be modified to usebasis functions other than sines, cosines, or equivalent exponentialforms that would perform the function of a Fourier Transform but notnecessarily be defined as a Fourier Transform. Neural networks or otherstatistical methods could also be used to convert the data to thespectral domain without the use of the Fourier Transform as typicallymathematically defined. Other conversion techniques can be used inaddition to, or in place of, a Fourier transform; despite this type ofinstrument being commonly known as a Fourier transform spectrometer, theimage processor 342 need not necessarily perform a Fourier transform onthe interference pattern image 338.

FIG. 4 illustrates an embodiment of a Fabry-Perot interferometer 420that can be used in the Fourier transform spectrometer 350 of FIG. 3.The Fabry-Perot interferometer 420 includes a first optical surface 454and a second optical surface 458, which are both partially transmissiveand partially reflective to the light whose spectral content is to bemeasured. In some embodiments, the first optical surface 454 is the rearsurface of a first optical element 452 located along the optical axis466. The second optical surface 458 can be, for example, the frontsurface of a second optical element 456 located along the optical axis466. In some embodiments, the optical axis 466 is orthogonal to adetector (not shown in FIG. 4) to which light from the Fabry-Perotinterferometer 420 is directed, whether by transmission or reflection,after having passed through the interferometer 420.

The first and second optical surfaces 454, 458 jointly define a resonantcavity 460 between themselves. As illustrated in FIG. 4, the gap 462between the first and second optical surfaces 454, 458 varies in atransverse direction that is substantially orthogonal to the opticalaxis 466. Specifically, the gap 462 varies in the x-direction, while theoptical axis 466, along which light travels through the Fouriertransform spectrometer, extends longitudinally in the z-direction. Insome embodiments, the gap 462 varies in a direction with respect to theoptical axis 466 that corresponds to the direction in which detectorelements (e.g., pixels) of the detector are arranged with respect to theoptical axis.

In the particular embodiment illustrated in FIG. 4, the first opticalsurface 454 is substantially planar and the first optical element 452 isa plate. Meanwhile, the second optical surface 458 includes two angledplanar segments that join at a vertex area 464, and the second opticalelement 456 is a prism. The vertex area 464 of the prism 456 is inoptical contact with the first optical surface 454 near the location 464where the optical axis 466 intersects the interferometer 420, thoughthis is not required. In some embodiments, the prism 456 includes a flatportion at the vertex area 464 in order to facilitate optical contactbetween the first and second optical elements 452, 456. While the secondoptical surface 458 is illustrated as being made up of two segments,either optical surface could be made up of any number of segments.

Although the first and second optical surfaces 454, 458 of theFabry-Perot interferometer 420 are illustrated as being planar orpiecewise planar, this is not required. Indeed, the first and secondoptical surfaces 454, 458 can have any shape so long as the gap 462between them varies as a function of location (e.g., transverse to theoptical axis) within the resonant cavity 460. For example, the firstand/or second optical surfaces 454, 458 can be linear, curvilinear, orpiecewise combinations of linear and curvilinear segments. In addition,the first and/or second optical surfaces 454, 458 can be smooth,discontinuous, pointed, etc.

The width of the gap 462 varies as a function of position in thex-direction within the resonant cavity 460. The precise variation of thegap width 462 is dependent upon the shape of the first and secondoptical surfaces 454, 458 and how they vary with respect to one another.In some embodiments, the gap width varies linearly, as illustrated bythe Fabry-Perot interferometer 220 shown in FIG. 2, or piecewiselinearly, as illustrated by the Fabry-Perot interferometer 420 shown inFIG. 4. This linear variation in the gap width can be caused by a linearslope of one or both of the optical surfaces 454, 458, or by opticalsurfaces with more complex shapes which, together, still result in alinear variation in gap width.

Linear variation in the gap width is not required, however. In fact, thevariation of the width of the gap 462 can be non-linear or arbitrary.The variation in gap width can be, for example, linear or have ahigher-order representation. The slope of the optical surfaces 454, 458with respect to one another can be set, in conjunction with, forexample, the pitch of detector elements, to determine the wavelengthrange over which the Fourier transform spectrometer can operate. Steepersloping surfaces create higher frequency spatial fringes in theinterference pattern, which can result in higher frequency spectralcontent.

As already discussed, the gap width between the optical surfaces of theFabry-Perot interferometer need not necessarily vary linearly orpiecewise linearly (e.g., in the direction orthogonal to the opticalaxis of the instrument). If, however, the spatial variation of the gapwidth is known, regardless of the shape, the spectrum of the input lightcan be accurately reconstructed in post-processing. While non-linearspatial variation in the gap width may distort the resultinginterference pattern, such distortion can be corrected based on accurateknowledge of the gap width variation as a function of spatial position.

In some embodiments, the gap in the resonant cavity 460 can have aminimum value of zero, which can be achieved at, for example, the center(e.g., 464) of the interferometer 424 or one or more other locations(e.g., peripheral portions of the interferometer 424). Alternatively,the gap in the resonant cavity 460 can have a non-zero minimum value atone or more locations, and the first and second optical elements 452,456 can be held in the desired position with respect to one another byappropriate structural supports.

In some embodiments, the first and second optical surfaces 454, 458 haveone or more locations where they physically contact one another. In suchembodiments, the gap 462 between the first and second optical surfaces454, 458 may approach but not exactly reach zero. In other embodiments,however, the first and second optical surfaces 454, 458 have one or morelocations where they are in optical contact with one another such thatthe gap 462 between them does reach zero. Optical contact between thefirst and second optical surfaces 454, 458 can be achieved in severalways, including applying pressure to force the first and second opticalelements 452, 456 against one another, applying index-matching opticalcement at the contact location(s), etc. Thin films of metals or metaloxides can also be used. In still other embodiments, however, the firstand second optical surfaces 454, 458 do not contact one another. In FIG.4, the first and second optical surfaces 454, 458 are in optical contactwith one another at the center of the Fabry-Perot interferometer.However, other designs could be used in which the first and secondoptical surfaces 454, 458 optically contact one another at otherlocations or not at all.

As already discussed, the gap between the first and second opticalsurfaces 454, 458 varies spatially in at least one direction.Specifically, in the embodiment illustrated in FIG. 4, the gap varies inthe x-direction, which is transverse to the longitudinal z-direction andthe optical axis 466. The gap between the first and second opticalsurfaces 454, 458 can vary in other directions as well. For example, thegap 462 may also vary, for example, in the y-direction in addition tothe x-direction. In such embodiments, the interference pattern createdby the Fabry-Perot interferometer 420 can have fringes formed inmultiple directions so as to enable the spectral content of the lightsource to be resolved in multiple directions. In some embodiments, thevariation in gap width is symmetric about the optical axis 466, thoughthis is not required.

The resonant cavity 460 can be vacuum sealed, or can be filled with agas (e.g., air) or liquid. Alternatively, the resonant cavity can befilled with a solid material. In such embodiments, the first and secondoptical surfaces 454, 458 can be front and rear surfaces of a singleoptical element.

The interference pattern created by the Fabry-Perot interferometer 420is a pattern of lighter and darker fringes. The fringes may be, forexample, spatially periodic. A detector with an array of detectingelements (e.g., pixels) can be positioned with respect to theFabry-Perot interferometer 420 so as to form an image of theinterference pattern. In some embodiments, each of the detectingelements substantially simultaneously samples the interference patternat a different spatial location.

In some embodiments, the Fourier transform spectrometer (e.g., 350)and/or the Fabry-Perot interferometer (e.g., 420) described hereincontain no moving parts. Alternatively, the first and second opticalsurfaces 454, 458 of the Fabry-Perot interferometer (e.g., 420) may bemovable with respect to one another. For example, the first and secondoptical surfaces 454, 458 can be moved longitudinally in the z-directionalong the optical axis 466, or tilted with respect to one another, so asto adapt the interferometer to various applications. Such movement canbe provided by, for example, a piezoelectric transducer, a precisionmotor, etc. It is important to note, however, that even in suchembodiments the gap between the first and second optical surfaces 454,458 varies spatially as discussed herein. Moreover, it is important tonote that such embodiments do not require movement of the first andsecond optical surfaces 454, 458 with respect to one another, or anyother time-varying characteristic of the interferometer (e.g., 420), inorder to collect the information needed to determine the spectralcontent of the input light.

Unlike other types of Fourier transform spectrometers which may usescanning Fabry-Perot interferometers, embodiments of the Fouriertransform spectrometer described herein do not require that anycharacteristic of the Fabry-Perot interferometer (e.g., gap width, indexof refraction, angle of orientation, etc.) be temporally varied in orderto measure an interferogram which can be processed to reveal thespectrum of the input light. Thus, while some embodiments of theFabry-Perot interferometer (e.g., 420) described herein may be capableof controlled temporal variation of some characteristic, such as therelative position of the first and second optical surfaces (e.g., 454,458), each interferogram that is collected for the purpose of analyzingthe spectral content of input light is captured without intentionallytemporally varying the relative position of the optical surfaces or anyother characteristic of the Fabry-Perot interferometer while theinterferogram is being captured.

FIG. 5 illustrates another embodiment of a Fabry-Perot interferometer520 that can be used in the Fourier transform spectrometer 350 of FIG.3. The Fabry-Perot interferometer 520 likewise includes first and secondoptical surfaces 554, 558 that create a resonant cavity 560therebetween. In addition, the first optical surface 554 is thesubstantially planar rear surface of an optical plate 552 that isdisposed orthogonal to the optical axis 566 of the interferometer 520.The second optical surface 558, however, is the convex portion of aplano-convex lens 556. In some embodiments, the lens 556 is acylindrical lens, though it could also be spherical or aspherical, forexample.

The Fabry-Perot interferometer 520 is formed by bringing the lens 556into optical contact with the plate 552. In this manner, a resonantcavity 560 is formed between the first and second optical surfaces 554,558. In this case, the gap 562 between the first and second opticalsurfaces 554, 558 varies non-linearly in the x-direction, which isorthogonal to the optical axis 566. The gap 562 is zero at the location564 where the optical axis 566 intersects the resonant cavity 560. Thisnon-linear variation in the gap width can lead to some distortion in theinterference pattern produced by the Fabry-Perot interferometer 520.However, since the spatial variation of the gap width is known, itseffect on the interference pattern can be calculated and corrected inpost-processing. Thus, non-linearly varying gaps may create interferencepatterns that can be linearized for further processing if so desired.

FIG. 6 is a schematic diagram of a Fourier transform spectrometer 650that uses a Fabry-Perot interferometer 620 with a spatially varying gap,and that includes a light collection optical system 670, and aninterference pattern relay optical system 675. The Fabry-Perotinterferometer 620 has first and second optical surfaces 654, 658, asdiscussed herein. The light collection optical system 670 can includeone or more optical elements (e.g., lens elements) for collecting lightfrom a source and directing it toward the Fabry-Perot interferometer 620in a suitable manner, depending upon the application. For example, insome embodiments, the light collection optical system 670 is configuredto image a light source onto the Fabry-Perot interferometer 620. In suchembodiments, the focal length and other characteristics of the lightcollection optical system 670 are set so that the source and theFabry-Perot interferometer 620 are located at conjugate optical planes.In other embodiments, the light collection optical system may beconfigured to form a collimated input beam for the interferometer 620.It should also be understood, however, that some embodiments of theFourier transform spectrometer described herein do not include a lightcollection optical system.

The interference pattern relay optical system 675 can be used to relaythe interference pattern formed by the Fabry-Perot interferometer 620 tothe detector 640. It can include one or more optical elements (e.g.,lens elements), and can be configured, for example, such that thedetector 640 and the Fabry-Perot interferometer 620 are located atconjugate optical planes. In some embodiments, the relay optical system675 and the detector 640 are integrated as a camera. In someembodiments, the Fabry-Perot interferometer with spatially varying gap620 can likewise be integrated into such a camera. In some embodiments,the detector 640, the interference pattern relay optical system 675, theFabry-Perot interferometer 620, and the light collection optical system670 share a common optical axis 666.

The Fabry-Perot interferometer 620 may cause double images to be formedat the detector. However, such double images, as well as additionalFresnel interference, can be managed by, for example, allotting enoughspace at optical contact so that the beams do not recombine at thedetector. In some embodiments, an advantage of using a relay opticalsystem 675 to transfer the interference pattern from the interferometer620 to the detector 640 is that a relatively slow beam can be used atthe input side of the interferometer, and magnification can raise thefinal f-number presented to the detector to enhance sensitivity.

It should be understood that some embodiments of the Fourier transformspectrometer described herein do not include an interference patternrelay optical system. In such embodiments, for example, the detector 640may be located in close enough proximity to the Fabry-Perotinterferometer 620 that the interference pattern generated by theinterferometer can be satisfactorily captured by the detector 640without the use of optics for transferring the interference pattern tothe detector. For example, the detector 640 may be placed in opticalcontact with the Fabry-Perot interferometer 620. In some embodiments, afilter, such as a Bayer filter or other filter mask, or other opticalcomponent can additionally be provided between the Fabry-Perotinterferometer 620 and the detector 640.

In some embodiments, the Fourier transform spectrometer 650 includes ascanner for scanning the field of view of the spectrometer over asurface to be imaged. For example, the scanner could scan the field ofview of the spectrometer in a direction that is both orthogonal to theoptical axis of the instrument and to the transverse direction in whichthe gap width of the Fabry-Perot interferometer 620 varies.

Usage of a Fabry-Perot interferometer with a spatially varying gap in aFourier transform spectrometer leads to several design considerations,which will be discussed with respect to FIGS. 7-14.

FIG. 7 is an example plot 700 that illustrates the transmission ofmonochromatic light through a Fabry-Perot interferometer with aspatially varying gap between two optical surfaces, the transmissionbeing shown for a range of reflectance values of the optical surfaces.Transmission through the interferometer is plotted as a function ofposition (e.g., in the direction in which the gap thickness of theFabry-Perot interferometer varies) and is normalized to unit modulationof peaks compared to troughs. Each of the transmission curves 701-705 onthe plot 700 represents a different reflectance value for the opticalsurfaces of the Fabry-Perot interferometer. The most sinusoidal-likefunction (i.e., curve 701) occurs with very low layer reflectance, whilehigh reflectance produces periodic narrow peaks (i.e., curve 705).

Since the periodic signal from a Fabry-Perot interferometer or etalonwith a spatially variable gap is not a pure sinusoid, the Fouriertransform of an interference pattern produced by the device for amonochromatic input signal exhibits sidelobes at integer multiples ofthe major frequency, reflecting the presence of the multiple passesthrough the interferometer.

FIG. 8 is an example plot 800 that illustrates the Fourier transform ofthe curve from FIG. 7 that corresponds to a Fabry-Perot interferometerhaving 18% reflecting optical surfaces. The magnitude of the Fouriertransform is plotted as a function of frequency, both in arbitraryunits. The main, fundamental frequency 810 is at +/−0.3 units, andhigher order sidelobes 820, 830 are apparent at higher frequencies.Specifically, given the periodic nature of the interference pattern, afirst sidelobe 820 appears at 0.6 units and a second sidelobe 830appears at 0.9 units, which are both integer multiples of thefundamental frequency. The peak 840 at zero frequency is due to a smallDC offset in the input function.

The higher order sidelobes 820, 830 may represent intolerable spectralcontamination if the bandwidth of the sidelobes is large enough tooverlap with the main frequency content. The higher order sidelobes 820,830 may, therefore, provide some constraints on the Fourier transformspectrometer described herein. If the sidelobes are large with respectwith some metric depending on the application, the uncontaminatedportion of the spectrum (between the sidelobes) may be a factor of twoof a designed wavelength. Thus, in some embodiments, the Fouriertransform spectrometer (e.g., 350) is limited to factors of two inwavelength.

FIG. 9 is an example plot 900 that illustrates the peak Fouriermagnitude 910 of a monochromatic source as a function of surfacereflectance for a Fabry-Perot interferometer that has a spatiallyvarying gap. The curve 910 reflects competing influences of totalreflectance, non-sinusoidal behavior, and modulation efficiency.

The reflectance of the surface layers (e.g., 454, 458) of theFabry-Perot interferometer (e.g., 420) which produces the maximum signalin the interference pattern image is a compromise between threecharacteristics of the interferometer: The net reflectivity (controllingthe rejection of input photons), the fringe contrast that contains theinterpretable spectral signal, and leakage of signal power intosidelobes. It is assumed, merely for the sake of analysis, that the netefficiency of the Fabry-Perot interferometer versus layer reflectivitycan be characterized by the peak magnitude of the Fourier transform ofthe interference pattern image that results from a monochromatic inputsignal. At very low layer reflectance, peak-to-trough modulation is low,so signal is low. At very high reflectance the device rejects most inputphotons and exhibits extreme sidelobes so efficiency is also low. Inbetween these extremes there is a maximum.

The plot 900 in FIG. 9 illustrates how one measure of efficiency of theFabry-Perot interferometer varies as a function of layer reflectance. Asjust discussed, the efficiency, as measured by maximum Fouriermagnitude, is lower for both high and low layer reflectances. Theplotted efficiency 910 shows a relative maximum near 40% reflectance.Thus, in some embodiments, the first and second optical surfaces (e.g.,454, 458) of the Fabry-Perot interferometer (e.g., 420) are providedwith a reflectance of approximately 40% in order to increase or maximizeefficiency. In some embodiments, the first and second optical surfacesof the Fabry-Perot interferometer are provided with a reflectance in therange of approximately 20%-60%. In some embodiments, the first andsecond optical surfaces are provided with a reflectance in the range ofapproximately 10%-70%. One or both of the first and second opticalsurfaces may have a reflectance in these ranges. Moreover, both opticalsurfaces may have substantially the same reflectance, or they may havedifferent reflectance values. In some embodiments, the reflectance ofthe first and second optical surfaces of the Fabry-Perot interferometeris set by using uncoated materials whose refractive indexes provideFresnel reflectance of the desired level. Alternatively, and/or inaddition, the first and second optical surfaces can be provided withmetal and/or dielectric coatings to achieve the desired reflectancevalues.

The metric illustrated in FIG. 9 is relative, adequate to specify layerreflectances which yield relatively higher efficiencies, but not topredict radiometric performance quantitatively, which involves a measureof absolute efficiency. The absolute efficiency can be defined, merelyfor the sake of analysis, as the product of the modulation efficiency ofthe fringes in the interference pattern produced by the Fabry-Perotinterferometer, and the peak signal, where the latter is normalized to100% modulation and the efficiency at zero reflectivity (true sinusoid).The peak signal term includes the losses due to reflectivity andsidelobe terms, as discussed herein. For the purposes of this analysis,the modulation is defined as the difference between the maximum andminimum of the signal, normalized to the maximum signal. The normalizedpeak intensity is the peak magnitude of the Fourier transform of amonochromatic input to Equation 1, with inputs normalized to 100%modulation, and output normalized to the response to a pure sinusoid.

FIG. 10 is an example plot 1000 that shows an estimate of absoluteefficiency 1030 for a Fourier transform spectrometer that uses aFabry-Perot interferometer with a spatially varying gap. The curve 1010that peaks at zero reflectance is the magnitude of the Fourier transformof the interference pattern which results from a monochromatic input,this time with the input normalized to 100% modulation, and with theoutput normalized to the output of a pure sinusoid. The curve 1020 thatpeaks at 100 percent reflectance is the modulation efficiency. The thirdcurve 1030 is the efficiency estimate, which is the product of the twoother curves 1010, 1020. The efficiency estimate 1030 indicates thatefficiency of the Fabry-Perot interferometer peaks near 40% reflectance,with a maximum efficiency near 70%, according to this particularestimate.

FIG. 11 is an example interference pattern image 1100 from a Fabry-Perotinterferometer with a spatially varying gap that illustrates the effectof incidence angle on the fringe period for a monochromatic input beam.As discussed herein, in some embodiments, the Fabry-Perot interferometeris used at an image plane of a light collection optical system (e.g.,670). Each point in the image is made up of light rays converging from arange of different angles, the range of angles being dependent upon theimaging optics. In such embodiments, the imaging of light at theFabry-Perot interferometer (e.g., 620) causes light that is ultimatelyincident upon a single pixel in the detector array (e.g., 640) to havetraversed the Fabry-Perot interferometer (e.g., 620) over a range ofangles. This affects the interference pattern because the fringe periodof the interference pattern created by the interferometer is a functionof the angle at which light traverses the interferometer.

If the fringe period is defined as the spacing between adjacent maxima,transmission maxima occur where the cosine of the phase difference δ isunity (Equation 1), and δ itself has a value of π(N+1/2), where N is aninteger. From Equation 2, the fringe spacing is proportional to a unitdifference between the values of N. Using N=0 (δ=π/2) and N=1 (δ=3π/2),the result after simplification is:

$\begin{matrix}{{{\Delta\; l} = {{\frac{\lambda}{{4\;\cos\;\theta}\;}\mspace{14mu} P} = {S\frac{\lambda}{{4\;\cos\;\theta}\;}}}}\mspace{11mu}} & (3)\end{matrix}$where Δl is the gap difference from peak to peak, P is the spatialperiod in micrometers, λ is the wavelength in micrometers, and S is theslope of the variable gap. Because the fringe period is a function ofthe angle at which rays traverse the gap between the optical surfaces ofthe Fabry-Perot interferometer, a range of angles at a given pointcauses a range of fringe periods to be measured at that point. If theinterference pattern is imaged by a practical camera with a finitef-number, each pixel will collect light resulting from a range ofincidence angles. Accordingly, these fringe patterns, with a range ofperiods, sum at the detector. As illustrated in FIG. 11, the fringeperiod of the interference pattern increases with increasing incidenceangle. Accordingly, as shown in the figure, the fringes begin to bendaway from the vertical for higher incidence angles as the period of eachfringe becomes larger.

The mix of light at each pixel of the detector that has traversed theFabry-Perot interferometer at different angles may limit the resolutionof the instrument in two ways. First, a narrow-band input optical signalwill be broadened in the final measured spectrum, as the transform fromthe spatial domain of the image data to the frequency domain of thespectral data will place the signal at slightly different frequenciesdepending on the zone of the light collection lens from which a givenray passed to the interferometer. Second, when the light rays at eachdetector pixel are summed over a range of angles, a null can form wherethe phase of the extreme angles are out of phase by 180 degrees.

FIG. 12 is an example interference pattern image 1200 that shows thesignal at each incidence angle integrated over the range from 0° to thegiven incidence angle. As illustrated, a null occurs toward the edges ofthe frame as incidence angle increases due to the signals at the extremeangles going out of phase and canceling. The null can be observedexperimentally, and can be taken as the resolution limit, for someapplications, of the Fabry-Perot interferometer with a spatially varyinggap that is described herein. The null can be expressed as a function ofthe extreme angles present. In an unobscured optical system, one extremeis 0 degrees (e.g., the optical axis). In a system with a centralobscuration, the value would be at some other angle. The other extrememay be defined by, for example, the f-number of the light collectionoptical system.

The null occurs when the number of fringes at θ₁ is equal to the numberof fringes at θ₂, plus one half, and is:

$\begin{matrix}{{FP}_{1} = {{{FP}_{2} + {\frac{P_{2}}{2}\mspace{14mu}{or}\mspace{14mu} F}} = \frac{P_{2}}{2\left( {P_{1} - P_{2}} \right)}}} & (4)\end{matrix}$where F is the number of fringes, and the subscripts indicate theextreme angles. Assuming an unobscured system (θ₁=0), the number offringes to reach the null is:

$\begin{matrix}{{F = \frac{1}{{{2\cos\mspace{11mu}\theta_{2}} - 1}\;}}\mspace{11mu}} & (5)\end{matrix}$

The resolution is tightly coupled with the number of fringes observed.Conventionally, the resolution of an FTS is:

$\begin{matrix}{{\Delta\;\sigma_{c}} = \frac{\sigma_{c}}{M}} & (6)\end{matrix}$where δσ_(c) is the resolution in wavenumbers, σ_(c) is the “cutofffrequency” (the highest frequency measurable by the system) at Nyquistsampling (two samples/period) to avoid aliasing, and where M is thenumber of samples in a single sided interferogram. At Nyquist sampling,by definition the number of samples M is twice the number of fringes F,so the spectral resolution R (λ/Δλ or σ/Δσ) is:

$\begin{matrix}{R = {\frac{\sigma_{c}}{\Delta\;\sigma_{c}} = {2\; F}}} & (7)\end{matrix}$

Using Equation 7, the resolution attainable with a Fabry-Perotinterferometer having a spatially varying gap is shown in FIG. 13. FIG.13 is an example plot 1300 that shows the resolving power 1310, as afunction of f-number of the input light, for a Fabry-Perotinterferometer with a spatially varying gap filled with air. Theresolving power 1310 is based on the position of the null, as describedherein. Usable resolutions in some applications (e.g., on the order of1%) are available at relatively low f-numbers. Spectral resolutionsutilized by many remote sensing systems (e.g., on the order of 100) canbe achieved with relatively modest f-numbers of the light collectionoptical system (e.g., 670). In some embodiments, the f-number of thelight collection optical system (e.g., 670) is in the range ofapproximately 0.5 to 20.

The resolution performance of the Fabry-Perot interferometer with aspatially varying gap may be enhanced, as compared to the air-filledgap, if the gap is filled by a solid, liquid, gel, etc. with arelatively high index of refraction. FIG. 14 is an example plot 1400that shows the resolving power 1410, as a function of the effectivef-number of the input light, for a germanium Fabry-Perot etalon with aspatially varying gap. The high refractive index of germanium has apowerful effect on the achievable resolving power. Of course, othermaterials besides a germanium could also be used to enhance theresolution of the instrument, as compared to the air-filled gap.

A relatively high index material in the gap of the Fabry-Perotinterferometer improves resolution because the angle θ in Equation 1 isthe internal angle of light in the interferometer. In a Fabry-Perotetalon (where the gap is filled), the refractive index of the fillingmedium makes this angle less than the incidence angle, according toSnell's law. Thus, the refractive index of the medium in the gap betweenthe optical surfaces influences the resolution. While high indexmaterials in the gap can be used to achieve relatively high resolutionsin theory, in practice, pixel counts of the detector may limit theresolution before the effective f-number of the input beam does.However, Fabry-Perot etalons with a spatially varying gap made of a highindex material could still be used, for example, to measure partialinterferograms. One such application is the detection of a specific gaswith fine spectral structure within a very narrow band.

The peak efficiency (combining the effects of reflectance, sidelobes andvariable modulation) near 70% is combined with the impact of theroll-off of amplitude toward the null. This roll-off is estimated tocause another approximately 50% loss, resulting in a final efficiency ofapproximately 35%. The roll-off is wavelength-dependent as shorterwavelengths may illuminate less than the full array of pixels dependingon the F-number and slope S; our estimate of 35% total efficiencyassumes placing the null at the full width of the array, for anintermediate wavelength. Longer wavelengths will experience lessroll-off attenuation and shorter wavelengths more, proportional to theirwavelength. These basic calculations suggest that a useful spatial FTScould be produced from a Fabry Perot interferometer or etalon withvariable gap thickness.

FIGS. 15-21 illustrate an experimental set-up of an embodiment of theFourier transform spectrometer described herein, as well as experimentalresults obtained using the set-up. In one experiment, the Fouriertransform spectrometer was used to measure the spectrum of fluorescentillumination that, while appearing white, is composed of narrow emissionlines. FIG. 15 is an example plot 1500 that shows the measured spectrumof fluorescent light using a Fourier transform spectrometer with aFabry-Perot interferometer that has a spatially varying gap. The plot1500 in FIG. 15 was generated using the apparatus shown in FIG. 16.

FIG. 16 is a photograph 1600 of an embodiment of a Fourier transformspectrometer that uses a Fabry-Perot interferometer with a spatiallyvarying gap. Starting from the top, FIG. 16 shows an Infrared camera, IRcamera lens, IR relay lens, interferometer, filter, and blackbodysource. The interferometer in FIG. 16 was constructed using acylindrical lens and a plate, both made of optical glass. Thecylindrical lens and plate were brought into optical contact to producea spatially variable air gap, as illustrated in FIG. 5. The uncoatedglass surfaces of the cylindrical lens and plate, which have 4%reflectance, served as the first and second optical surfaces (e.g., 554,558) of the Fabry-Perot interferometer. The gap separation between thecylindrical lens and the plate was not linear, but the radius of thelens allowed linearization of the fringe pattern. Owing to therelatively low reflectance of the surfaces, the experimental Fabry-Perotinterferometer produced modest modulation (about 20%).

With reference to FIG. 15, the Fabry-Perot interferometer of FIG. 16 wasused to analyze the spectrum of fluorescent light. The interferencepattern created by the Fabry-Perot interferometer was viewed inreflectance rather than transmission, employing a dark background toimprove visual contrast. The interference pattern produced by theinterferometer was plainly visible, with vivid colors enabled by thefluorescent source that emits narrow spectral lines, and well-separatedfringes. Images of the interference pattern were captured. The fringeprofiles were extracted, linearized, and then transformed into thespectral domain to produce the spectrum shown in FIG. 13. The dottedline 1520 illustrates the radiance spectrum of the fluorescent sourcereflected off of a Lambertian surface, as measured by a commercialgrating spectrometer. The solid line 1510 illustrates the spectrum thatwas measured using the experimental version of a Fourier transformspectrometer with a Fabry-Perot interferometer that has a spatiallyvarying gap. Specifically, the solid line 1510 illustrates the Fouriertransform of the linearized fringe pattern observed in theinterferometer, calibrated with a laser source. While the resolution isrelatively low, the spectral lines of the fluorescent source areresolved.

In a second experiment, a 1-m focal length ZnSe cylindrical lens andflat ZnSe plate, both uncoated, were used to produce a Fabry-Perotinterferometer with a spatially varying gap. Owing to the relativelyhigher reflectance of the ZnSe surfaces (approximately 18%), themodulation was on order 50%, and the interference pattern was viewed intransmission. The Fabry-Perot interferometer was imaged onto acommercial microbolometer array camera using a pair of opposing 50 mmf/1.4 IR camera lenses backlit by a 100 degree Celsius flat plateblackbody. The fringe pattern imposed by the blackbody source is shownin FIG. 15.

FIG. 17 is an example interference pattern image 1700 obtained using theFourier transform spectrometer of FIG. 16. The broad central fringe isconsistent with the nonlinear variation of the gap of the ZnSeFabry-Perot interferometer transverse to the optical axis. A narrow-band10.45 micrometer interference filter was placed in the beam to providewavelength calibration, and to provide data to linearize the fringepattern. Using these data, the system wavelength response (thecombination of the wavelength sensitivity of the camera, principally,and the weak wavelength variations of the interferometer and the cameralenses) was derived.

In an additional experiment, the experimental Fabry-Perot interferometerwas used to obtain the spectrum of a flowing gas, in this case diethylether. FIG. 18 is an example plot 1800 of the measured spectrum of ablackbody source with diethyl ether sprayed into the beam, which wasobtained using the Fourier transform spectrometer of FIG. 16. Diethylether, as a relatively strong IR absorber, was used to show that theFabry-Perot interferometer with a spatially varying gap could capturethe spectrum of a specific chemical. The curve 1810 represents themeasured spectrum of the black body radiation before introducing thediethyl ether gas. While the IR camera was running and collectinginterferograms, the gas was introduced into the beam, and the fringeresponse was immediately apparent, as illustrated by the curve 1820.Using the same procedure used to produce the blackbody spectrum(convolved with camera response), the gas absorption lines are apparentand are superimposed on the blackbody response curve 1810. FIG. 19 is anexample plot 1900 that shows the time variation of the measured spectrumfrom FIG. 18.

In another experiment, a Fabry-Perot interferometer with a linear gapwas created. A prism with a relatively shallow included angle (32 mrad)was created from uncoated ZnSe. This prism was brought into contact witha flat ZnSe plate, as illustrated in FIG. 4.

FIG. 20 is an example interference pattern image 2000 produced by aFourier transform spectrometer with a Fabry-Perot interferometer thathas a linearly spatially varying gap. The interference pattern image2000 shows the response of the prism-plate interferometer to a 10.45micron, 50 nm wide input. Near the center of the image the fringes aresomewhat distorted probably owing to poor optical contact. The fringesdisplay a dropoff in intensity toward the edges of the frame. Thegradual loss of fringe visibility away from the center shows the nullthat results from the range of incidence angles through theinterferometer, as discussed herein. The null was consistent with thef/1.4 input beam that was used. The fringe period is linear withposition.

FIG. 21 is an example plot 2100 of the measured spectrum 2110 of ablackbody source with diethyl ether sprayed into the beam, which wasobtained using a Fourier transform spectrometer with a Fabry-Perotinterferometer that has a linearly spatially varying gap. Thisexperiment was performed similarly to the one illustrated in FIG. 18.However, in this case, the response of the system was plotted asrelative absorbance. The data were calibrated in wavelength using a 10.5micron filter, and non-uniformity in the response was removed using twoblackbody temperatures, 25 and 100° C.

Embodiments have been described in connection with the accompanyingdrawings. However, it should be understood that the figures are notdrawn to scale. Distances, angles, etc. are merely illustrative and donot necessarily bear an exact relationship to actual dimensions andlayout of the devices illustrated. In addition, the foregoingembodiments have been described at a level of detail to allow one ofordinary skill in the art to make and use the devices, systems, etc.described herein. A wide variety of variation is possible. Components,elements, and/or steps can be altered, added, removed, or rearranged.While certain embodiments have been explicitly described, otherembodiments will become apparent to those of ordinary skill in the artbased on this disclosure.

Depending on the embodiment, certain acts, events, or functions of anyof the methods described herein can be performed in a differentsequence, can be added, merged, or left out all together (e.g., not alldescribed acts or events are necessary for the practice of the method).Moreover, in certain embodiments, acts or events can be performedconcurrently or sequentially.

The processing, or processor, disclosed herein can be implemented using,for example, electronic hardware, computer software, or combinations ofboth. Whether such functionality is implemented as hardware or softwaredepends upon the particular application and design constraints imposedon the overall system. The described functionality can be implemented invarying ways for each particular application. In the case of software, asoftware module can reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, aCD-ROM, or any other form of computer-readable storage medium known inthe art. A storage medium can be coupled to a processor such that theprocessor can read information from, and write information to, thestorage medium. In the case of hardware, the processor can beimplemented as a single processor computer chip, multiple computerchips, an ASIC, an FPGA, discrete components, or any other suitableprocessing device or equipment. In addition, the processor may bedirectly or remotely communicatively coupled (e.g., via a network suchas the Internet or a LAN) to the information source. The processor mayalso include a distributed computing cluster or grid.

While the above detailed description has shown, described, and pointedout novel features as applied to various embodiments, it will beunderstood that various omissions, substitutions, and changes in theform and details of the devices or algorithms illustrated can be madewithout departing from the spirit of the disclosure. As will berecognized, certain embodiments of the inventions described herein canbe embodied within a form that does not provide all of the features andbenefits set forth herein, as some features can be used or practicedseparately from others. The scope of certain inventions disclosed hereinis indicated by the appended claims rather than by the foregoingdescription. All changes which come within the meaning and range ofequivalency of the claims are to be embraced within their scope.

What is claimed is:
 1. A Fourier transform spectrometer, comprising: a Fabry-Perot interferometer to create a spatial interference pattern using input light; a detector positioned with respect to the Fabry-Perot interferometer to capture an image of the spatial interference pattern to produce an interferogram, the detector comprising a plurality of detection elements, and defining an optical axis that is orthogonal to the detector; and a processor that is communicatively coupled to the detector, the processor being configured to process the interferogram to determine information about the spectral content of the light, wherein the Fabry-Perot interferometer comprises first and second optical surfaces that are partially transmissive and partially reflective to the light, the first and second optical surfaces defining a resonant cavity therebetween, the distance between the first and second optical surfaces being spatially variable in a first transverse direction that is orthogonal to the optical axis, and wherein the first and second optical surfaces are configured such that the interferogram is symmetric.
 2. The Fourier transform spectrometer of claim 1, wherein the first and second optical surfaces are fixed with respect to one another.
 3. The Fourier transform spectrometer of claim 1, wherein the first and second optical surfaces have a smoothly varying slope in the first transverse direction.
 4. The Fourier transform spectrometer of claim 1, wherein the distance between the first and second optical surfaces is variable in a second transverse direction that is orthogonal to the optical axis and to the first transverse direction.
 5. The Fourier transform spectrometer of claim 1, wherein the distance between the first and second optical surfaces varies substantially linearly in the first transverse direction for at least a portion of the resonant cavity.
 6. The Fourier transform spectrometer of claim 1, wherein at least one of the first and second optical surfaces is substantially planar.
 7. The Fourier transform spectrometer of claim 1, wherein at least one of the first and second optical surfaces comprises two or more portions joined together at an angle.
 8. The Fourier transform spectrometer of claim 1, wherein at least one of the first and second optical surfaces comprises a prism, the prism comprising at least first and second substantially planar portions that join at a vertex region.
 9. The Fourier transform spectrometer of claim 1, wherein at least one of the first and second optical surfaces comprises a surface of a lens.
 10. The Fourier transform spectrometer of claim 9, wherein the lens is a cylindrical lens.
 11. The Fourier transform spectrometer of claim 1, wherein the distance between the first and second optical surfaces has a relative minimum in a central region of the Fabry-Perot interferometer.
 12. The Fourier transform spectrometer of claim 1, wherein the distance between the first and second optical surfaces has a relative minimum at a peripheral region of the Fabry-Perot interferometer.
 13. The Fourier transform spectrometer of claim 1, wherein the first and second optical surfaces are in physical contact with one another at one or more physical contact points.
 14. The Fourier transform spectrometer of claim 1, wherein the first and second optical surfaces are in optical contact with one another at one or more optical contact points where the optical distance between the first and second optical surfaces is substantially zero.
 15. The Fourier transform spectrometer of claim 1, wherein the region between the first and second optical surfaces comprises a vacuum, gas, or liquid.
 16. The Fourier transform spectrometer of claim 1, wherein the region between the first and second optical surfaces comprises a solid material.
 17. The Fourier transform spectrometer of claim 1, wherein the first and second optical surfaces have a reflectance in the range of about 20-60%.
 18. The Fourier transform spectrometer of claim 1, wherein the first and second optical surfaces have a reflectance of about 40%.
 19. The Fourier transform spectrometer of claim 1, further comprising an optical system to relay the interference pattern from the Fabry-Perot interferometer to the detector.
 20. The Fourier transform spectrometer of claim 1, wherein at least one of the first and second optical surfaces is movable.
 21. The Fourier transform spectrometer of claim 20, wherein at least one of the first and second optical surfaces is movable with respect to the other.
 22. The Fourier transform spectrometer of claim 21, wherein at least one of the first and second optical surfaces is movable with respect to the detector.
 23. The Fourier transform spectrometer of claim 21, wherein at least one of the first and second optical surfaces can be tilted with respect to the other.
 24. A method of determining the spectral content of input light, the method comprising: creating a spatial interference pattern from input light using a Fabry-Perot interferometer; creating an interference pattern image using a detector that is positioned with respect to the Fabry-Perot interferometer to capture an image of the spatial interference pattern to produce an interferogram, the detector comprising a plurality of detection elements, and defining an optical axis that is orthogonal to the detector; and processing the interferogram using a processor to determine information about the spectral content of the light, wherein the Fabry-Perot interferometer comprising first and second optical surfaces that are partially transmissive and partially reflective to the light, the first and second optical surfaces defining a resonant cavity therebetween, the distance between the first and second optical surfaces being spatially variable in a first transverse direction that is orthogonal to the optical axis, wherein the first and second optical surfaces are configured such that the interferogram is symmetric, and wherein the interferogram is captured during a period of time in which characteristics of the Fabry-Perot interferometer are not intentionally varied. 